Use of indirect addition in adults’ mental subtraction in the number domain up to 1,000

Torbeyns, Joke; Smedt, Bert De; Peters, Greet; Ghesquière, Pol; Verschaffel, Lieven

doi:10.1111/j.2044-8295.2011.02019.x

Cited by 17 publications

(38 citation statements)

References 27 publications

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“…First, research evidence shows that individuals have a preference for using the rule of addition to solve numerical problems (e.g., solving a simple subtraction problem by calculating how much should be added to the smaller number to arrive at the larger number). (45) In addition, Brown and Morley (2007) have found that individuals' estimates of perceived risk are not necessarily numerically specific, but are typically fuzzy and span a range of possible estimates. (36) Hence, many of our participants may have interpreted our scenarios as numerical problems and, consequently, employed an addition rule for convenience and to alleviate task complexity.…”

Section: Discussionmentioning

confidence: 99%

Do People Believe Combined Hazards Can Present Synergistic Risks?

2011

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The risk attributable to some hazard combinations can be greater than the sum of the risk attributable to each constituent hazard. Such "synergistic risks" occur in several domains, can vary in magnitude, and often have harmful, even life-threatening, outcomes. Yet, the extent to which people believe that combined hazards can present synergistic risks is unclear. We present the results of two experimental studies aimed at addressing this issue. In both studies, participants examined synergistic and additive risk scenarios, and judged whether these were possible. The results indicate that the proportion of people who believe that synergistic risks can occur declines linearly as the magnitude of the synergistic risk increases. We also find that people believe, despite scientific evidence to the contrary, that certain hazard combinations are more likely to present additive or weakly synergistic risks than synergistic risks of higher magnitudes. Furthermore, our findings did not vary as a simple function of hazard domain (health vs. social), but varied according to the characteristics of the specific hazards considered (specified vs. unspecified drug combinations). These results suggest that many people's beliefs concerning the risk attributable to combined hazards could lead them to underestimate the threat posed by combinations that present synergistic risks, particularly for hazard combinations that present higher synergistic risk magnitudes. These findings highlight a need to develop risk communications that can effectively increase awareness of synergistic risks.

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Section: Discussionmentioning

confidence: 99%

Do People Believe Combined Hazards Can Present Synergistic Risks?

2011

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“…Following a choice/no-choice design, Torbeyns, Ghesquière, et al (2009) and Torbeyns, De Smedt, Peters, Ghesquière, and Verschaffel (2011) empirically addressed adults' strategy use on multi-digit subtraction problems. In three subsequent studies, Torbeyns et al (2009Torbeyns et al ( , 2011 offered adults different types of multi-digit subtraction problems with numbers up to 1,000 in one choice and two no-choice conditions. In the choice condition, participants had to choose between direct subtraction and subtraction by addition.…”

Section: Previous Studies On Direct Subtraction Versus Subtraction Bymentioning

confidence: 99%

Subtraction by addition strategy use in children of varying mathematical achievement level: A choice/no-choice study

et al. 2018

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We investigated the use of the subtraction by addition strategy, an important mental calculation strategy in children with different levels of mathematics achievement. In doing so we relied on Siegler’s cognitive psychological model of strategy change (Lemaire & Siegler, 1995), which defines strategy competencies in terms of four parameters (strategy repertoire, distribution, efficiency and selection), and the choice/no-choice method (Siegler & Lemaire, 1997), which is essentially characterized by offering items in two types of conditions (choice and no-choice). Participants were 63 11-12-year-olds with varied mathematics achievement levels. They solved multi-digit subtraction problems in the number domain up to 1,000 in one choice condition (choice between direct subtraction or subtraction by addition on each item) and two no-choice conditions (obligatory use of either direct subtraction or subtraction by addition on all items). We distinguished between two types of subtraction problems: problems with a small versus large difference between minuend and subtrahend. Although mathematics instruction only focused on applying direct subtraction, most children reported using subtraction by addition in the choice condition. Subtraction by addition was applied frequently and efficiently, particularly on small-difference problems. Children flexibly fitted their strategy choices to both numerical item characteristics and individual strategy speed characteristics. There were no differences in strategy use between the different mathematical achievement groups. These findings add to our theoretical understanding of children’s strategy acquisition and challenge current mathematics instruction practices that focus on direct subtraction for children of all levels of mathematics achievement.

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“…While previous studies have shown that adults use the subtraction by addition strategy frequently, efficiently (i.e., fast and accurately), and flexibly (i.e., mainly, but not exclusively on problems with a relatively large subtrahend) (Peters, De Smedt, Torbeyns, Ghesquière, & Verschaffel, ,; Torbeyns, De Smedt, Peters, Ghesquière, & Verschaffel, ; Torbeyns, Ghesquière, et al ., ), well‐documented evidence on primary school children's self‐reported use of the subtraction by addition strategy when mentally solving two‐digit subtraction problems is limited (Blöte et al ., ; De Smedt et al ., ; Selter, ; Torbeyns et al ., ). For example, Torbeyns et al .…”

Section: Introductionmentioning

confidence: 96%

“…While previous studies have shown that adults use the subtraction by addition strategy frequently, efficiently (i.e., fast and accurately), and flexibly (i.e., mainly, but not exclusively on problems with a relatively large subtrahend) (Peters, De Smedt, Torbeyns, Ghesquière, & Verschaffel, 2010a,b;Torbeyns, De Smedt, Peters, Ghesquière, & Verschaffel, 2011;, well-documented evidence on primary school children's self-reported use of the subtraction by addition strategy when mentally solving two-digit subtraction problems is limited (Blöte et al, 2000;De Smedt 1 People can also use a third strategy, the so-called indirect subtraction strategy in which they determine how much needs to be subtracted from the minuend to get to the subtrahend (e.g., 75 À 43 = . by 75 À 30 = 45 and 45 À 2 = 43; so the answer is 30 + 2 = 32) (De Corte & Verschaffel, 1987).…”

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Children's use of addition to solve two‐digit subtraction problems

Peters

Smedt

Torbeyns

et al. 2012

British J of Psychology

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Subtraction problems of the type M - S = ? can be solved with various mental calculation strategies. We investigated fourth- to sixth-graders' use of the subtraction by addition strategy, first by fitting regression models to the reaction times of 32 two-digit subtractions. These models represented three different strategy use patterns: the use of direct subtraction, subtraction by addition, and switching between the two strategies based on the magnitude of the subtrahend. Additionally, we compared performance on problems presented in two presentation formats, i.e., a subtraction format (81 - 37 = .) and an addition format (37 + . = 81). Both methods converged to the conclusion that children of all three grades switched between direct subtraction and subtraction by addition based on the combination of two features of the subtrahend: If the subtrahend was smaller than the difference, direct subtraction was the dominant strategy; if the subtrahend was larger than the difference, subtraction by addition was mainly used. However, this performance pattern was only observed when the numerical distance between subtrahend and difference was large. These findings indicate that theoretical models of children's strategy choices in subtraction should include the nature of the subtrahend as an important factor in strategy selection.

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Use of indirect addition in adults’ mental subtraction in the number domain up to 1,000

Cited by 17 publications

References 27 publications

Do People Believe Combined Hazards Can Present Synergistic Risks?

Do People Believe Combined Hazards Can Present Synergistic Risks?

Subtraction by addition strategy use in children of varying mathematical achievement level: A choice/no-choice study

Children's use of addition to solve two‐digit subtraction problems

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